Problem: What do the following two equations represent? $-5x+y = 3$ $-2x-10y = -3$
Answer: Putting the first equation in $y = mx + b$ form gives: $-5x+y = 3$ $y = 5x+3$ Putting the second equation in $y = mx + b$ form gives: $-2x-10y = -3$ $-10y = 2x-3$ $y = -\dfrac{1}{5}x + \dfrac{3}{10}$ The slopes are negative inverses of each other, so the lines are perpendicular.